Part I. Long Term Perspective

All-in or Fold (AoF) is a relatively new game in the poker world. I have been playing amateur poker for many years, and I became interested in the profitability of playing AoF. After searching the Internet, I did not find a clear answer to this question. Specifically, I focused on the GG Network, which includes poker rooms such as GGPoker, GGPokerok, Natural8, GGPokerUkraine, and a few others.

The rules of AoF are quite simple. There are four players at the table, each of whom is dealt two cards. Based on these cards, players must decide whether to discard them and leave the game or keep them and go all-in, putting their entire stack into the pot. Then, five community cards are revealed. The winner is the player who has assembled the best combination according to the rules of Texas Hold'em.

The rules allow for a good modeling of the game and player behavior. The objective of the model is to determine the optimal strategy for maximizing profit. Profitability is primarily influenced by three factors:

• your skill level (how effectively you play);
• the skill level of your opponents;
• the amount of rake and commissions you pay, as well as the rakeback and bonuses you receive.

The aim of this publication is to demonstrate that regardless of your skill level, you will inevitably experience long-term losses.

Rake and commissions

Let's start with the last point. These are passive incomes and expenses, which practically do not depend on the quality of your game and the game of your opponents. They are determined by the house rules.

On the GG Network in AoF, commissions vary slightly on tables with different limits. For clarity, I will use the example of $0.5/$1 blinds and an $8 buy-in (stack). There are three types of commission for each hand:

• 0.05BB (big blind) rake;
• Jackpot fee of $0.05B;
• All-inFortune fee of $0.05 or the equivalent of0.05BB.

Now, regarding payouts (earnings). The size and rules of payouts are rather vague and depend entirely on your 'luck,' i.e., on the 'random' number generator (read: the goodwill of the poker room). There are three types of payouts:

1. Rakeback is paid based on the amount of rake you have paid and depends on the number of hands you have played and your 'luck,' the amount of which is determined by the poker room. The size of the rakeback varies from 10% to 60% of the rake. As a rule, players receive between 20% to 30%, sometimes 10%, and very rarely 50%. It's almost unheard of to receive 60% - you'd have to play all day long for several months and be extremely 'lucky.' In this model, I will use a rakeback of 50% of the rake paid to ensure that I am not underestimating the player's income.
2. The jackpot is paid out if you collect a straight flush combination, with both of your cards involved in the combination. The payout is 0.1% of the jackpot pot. The size of the pot varies, ranging from $400,000 to $900,000, with an average of around $600,000. Therefore, the jackpot payout will be approximately $600 or 600BV. Since the frequency of the jackpot depends on the connectors you play, the jackpot payout in the model is based on the number of straight flushes actually hit and played. This amount is then added to the player's profit after all hands.
3. In All-inFortune, the specific size, frequency, and rules of payouts are not described anywhere. It is only noted that they are determined randomly. Observations indicate that payouts are approximately 20-25% of this fee. In the model, we assume that payouts are 50%, again to avoid disadvantaging the player.

To summarize:

For rake and rakeback: –0.05ВВ + 0.025BB = –0.025BB.

For Jackpot: –0.05ВВ.

For All-inFortune: –0.05ВВ + 0.025BB = –0.025BB.

Putting it all together, you get a loss of 0.1BB on every hand, regardless of whether you participated in the pot or not. At a $0.5/$1 limit and buy-in of $8, this equals 10 cents per game.

Strength of opponents

Let's try to determine the strength of AoF players. To do this, we will use the available statistics on joining the bank (All-in). It is displayed on the table, to the left of the player. I collected statistics on over 400 players, mostly at the $0.5/$1 limit. The distribution of All-in statistics is shown in Fig. 1.

It looks like a Gaussian distribution. Let's test this hypothesis. For this purpose, let's apply the D'Agostino test. Indeed, the test shows that the distribution is Gaussian with a probability of more than 97%. Let's determine the mean and standard deviation of this distribution. The mean is 37.5824 and the standard deviation is 8.9203. In the future I will use the distribution with these parameters for modeling. The practical meaning of these values is that you will most often face a player with an All-in statistic of 37-38%, and the All-in rates of 2/3 of the players will be in the range of 28-47%.

Model

Modeling the game in AoF involves creating four players - one main player (Hero) and three opponents (Oppo).

Four types of players, using different strategies, were created to simulate the Nego game.

The first type, EV Nego, plays based on an EV (expectation of the hand) calculation. If the EV of an all-in is greater than the EV of a fold, Hero will bet, otherwise he will fold. EV fold is different for different positions of Hero at the table. The EVfold for the Catof, Batton, Small and Big blind are 0BB, 0BB, -0.5BB, -1BB respectively. The EV is calculated taking into account the statistics of the opponents and the probability of their actions. The jackpot influence on EV is calculated by adding the calculated value corresponding to the type of connectors.

The second type, HeroGTO, plays according to the GTO (optimal game theory) strategy. To account for the jackpot, the best connectors that form a straight flush are added to the strategy.

The third type, HeroABC, uses the simplest ABC poker strategy plus all the connectors that form a straight flush. That is, he will play 22+, A2s+, K9s+, Q8s+, J7s+, T6s+, 95s+, 84s+, 73s+, 62s+, 52s+, 42s+, 32s, ATo+, KJo+, QJo, regardless of position.

The last type is HeroFish. He always goes all-in with any cards and in any position.

Opponents play the percentage of the strongest hands set according to the all-in statistics. They also play connectors that form a straight flush: 43s+, 64s+, T7s+, J7s+, A2s-A5s. This set of connectors adds 10% to the all-in statistics. To compensate for this impact, the percentage of connectors is subtracted from the total statistics. For example, if the total all-in statistic is 40%, Orr will play 30% of the strongest hands and 10% of the connectors.

Game Simulation: There are two to four players at the table. One of them is of the Hero variety, the others are Oppo. The Oppo players are chosen randomly from the normal distribution described above. Every 20-30 hands, one of the Orro players is replaced or leaves the table. The model is played 60% of the time in foursomes, 30% in threesomes, and 10% in doubles. Ten million hands are played to get a stable performance.

Simulation Results

Here are the simulation results for the four Hero player types after ten million hands. Table 1 and Figure 2 display the players' winrate expressed in big blinds per 100 hands. The table also shows the all-in statistics for each type of strategy and the average number of games required to hit the jackpot.

Gamer type	Winrate without jackpot BB/100 hand	Winrate with jackpot BB/100 hand	All-in %	Average hands for jackpot
Hero EV	–5.4	–3.5	35.71	31250
Hero GTO	–6.6	–3.0	36.92	15625
Hero ABC	–19.8	–14.3	27.98	10204
Hero Fish	–59.0	–53.7	100	10204

In general, the results are quite sad, showing that even with optimal play (HeroEV, HeroGTO) with or without jackpot, you will always be in the negative in the long run. Changing the style of play (HeroABC, HeroFish) only leads to even bigger losses.

Conclusions

In the long run you will always lose, no matter how well you know how to play. Jackpot wins improve the situation a bit, but still don't make the game profitable. A winrate of 3-5BB losses per 100 hands would be a very good result.

Part 2 will look at the results of short-term play.